In this article, we propose a new wavelet method for solving nonlinear Katugampola fractional differential equations on an arbitrary interval. We have introduced a new wavelet, which we named as the Katugam-pola Gegenbauer wavelet (KGW), and constructed its new operational matrices of Katugampola fractional integrations as well as Katugampola fractional derivatives. The Katugampola Gegenbauer wavelet and its operational matrices are combined with the Adomian polynomials to propose a new method for the solution of nonlinear Katugampola fractional differential equations. The purpose of using the Adomian polynomials is to handle the nonlinearities in the equations. Furthermore, we have provided a detailed methodology for implementing the proposed approach to nonlinear Katugampola fractional differential equations. A detailed error analysis is also performed for the proposed method. The proposed method is implemented on several nonlinear Katugampola fractional differential equations to show the reliability, efficiency, and accuracy of the method.
Bint-e-Ali et al. (Fri,) studied this question.